6 papers · 1 filter
Spherical tropical curves are balanced
Desmond Coles
One of the characterizing features of tropicalizations of curves in an algebraic torus is that they are balanced. Tevelev and Vogiannou introduced a spherical tropicalization map f…
Towards the tropicalization of reductive groups
Desmond Coles, Martin Ulirsch
Let be a connected reductive algebraic group over an algebraically closed field of characteristic zero carrying the trivial valuation. In this article we discuss two candidates…
A construction of algebraizable formal models
Desmond Coles, Netanel Friedenberg
Let be a variety over a complete nontrivially valued field . We construct an algebraizable formal model for the analytification of in the case admits a closed embedd…
Spherical tropicalization and Berkovich analytification
Desmond Coles
Let be a spherical variety. We show that Tevelev and Vogiannou's tropicalization map from to its tropicalization factors through the Berkovich analytification $X^{\text{an}…
The moduli space of tropical curves with fixed Newton polygon
Desmond Coles, Neelav Dutta, Sifan Jiang +2
Given a lattice polygon, we study the moduli space of all tropical plane curves with that Newton polygon. We determine a formula for the dimension of this space in terms of combina…
Tropically planar graphs
Desmond Coles, Neelav Dutta, Sifan Jiang +2
We study tropically planar graphs, which are the graphs that appear in smooth tropical plane curves. We develop necessary conditions for graphs to be tropically planar, and compute…